Denition 2.6 (Markov Chain) For random variables X1 , X2 , , Xn , where
n 3, X1 ! X2 ! ! Xn forms a Markov chain if
p ( x 1 , x2 , , x n ) =
p( x 1 , x 2 ) p ( x 3 | x 2 ) p ( x n | x n
0
1)
if p(x2 ), p(x3 ), , p(xn
otherwise.
1)
>0
Remark X1 ! X2 ! X3 i
Chapter 2
Information Measures
Raymond W. Yeung 2014
The Chinese University of Hong Kong
Thursday, 26 December, 13
In this chapter basic tools
Thursday, 26 December, 13
In this chapter basic tools
Probability preliminaries
Shannons information measures
Chapter 1
The Science of Information
Raymond W. Yeung 2014
The Chinese University of Hong Kong
Information Theory
Information Theory
Founded by Claude E. Shannon (1916-2001)
The Mathematical Theory of Communication, 1948
Study fundamental limits in co
Proposition 2.5 For random variables X, Y , and Z , X
p(x, y, z ) = a(x, y )b(y, z )
for all x, y , and z such that p(y ) > 0.
Thursday, 26 December, 13
Z |Y if and only if
Proposition 2.5 For random variables X, Y , and Z ,
X ? Z |Y if and only if
p(x, y
Proposition 2.12 Let X1 , X2 , X3 , and X4 be random variables such that
p(x1 , x2 , x3 , x4 ) is strictly positive. Then
X1 ? X4 |(X2 , X3 )
X1 ? X3 |(X2 , X4 )
) X1 ? (X3 , X4 )|X2 .
See textbook for a proof of the proposition.
Not true if p is not st
2.3 Continuity of Shannons
Information Measures for Fixed
Finite Alphabets
Thursday, 26 December, 13
Finite Alphabet vs Countable
Alphabet
All Shannons information measures are continuous when the alphabets
are xed and nite.
For countable alphabets, Sha
Follow the Netiquette Rules for Success
With the onset of the online education environment and online courses a new buzzword
has evolved called, netiquette. Simply defined, it means etiquette on the Internet (or
net). In an online course you will have you
Problem #1:
Design a flowchart for a program that will read SALES from each record, print each sales
amount, and print the number of records read.
To begin we need to go through the four routine components and ask/answer questions about
each.
LOOP You nee
COURSE OUTLINE w/due dates CIS 1223 LOGIC & ALGORITHMS
Semester begins August 14th
Assignment
Due date
Getting Started Assessment / Student Introduction
Found in the Getting Started Course Menu
Chapter 1, Assignment #1 posted in Course Teaching Agenda
C
Getting Started Assessment.Youwillcompletethisassignmentbytypingyouranswers*only*
intheboxbelowthequestion.Yourassignmentwillbegradedandpostedtoyourgradebookwithin24
to72hoursaftertherequiredduedateandtime.CheckthepointsearnforthisspecificassignmentinMy
Problem #1:
Design a flowchart for a program that will read SALES from each record, print each sales
amount, and print the number of records read.
To begin we need to go through the four routine components and ask/answer questions about
each.
LOOP You nee
SimplificationwithBooleanProperties
Chapter5
Boolean(SetTheory)Properties
Properties that hold true are: (the Venn Diagram of each
proves its truth)
A B is the same as B A
Commutative
Associative (A B) C is the same as A (B
C)
Distributive A(BUC) is the s
Discussion forums, threads and posts
Review the following tutorials at http:/ondemand.blackboard.com/students.htm:
1. Create a Discussion Board Post
2. Reply to a Discussion Board Thread
3. Organizing Discussion Board Posts
4. Viewing Discussion Board Gra
Chapter 6
Truth Functional Logic and Decision Tables
Common words that translate as and
A and B
A but B
A yet B
A on the other hand B
A although B
A while B
A even though B
A as well as B
A nonetheless B
A despite the fact that B
(A ^ B )
Common words tha
Use the checklist below to make sure you have completed all the requirements for the
Getting Started Learning Module. All requirements must be completed no later than the
required due date and time posted on the Course Outline calendar
Check off each requ
Chapter 6
Truth Functional Logic and Decision Tables
Common words that translate as and
A and B
A but B
A yet B
A on the other hand B
A although B
A while B
A even though B
A as well as B
A nonetheless B
A despite the fact that B
(A ^ B )
Common words tha
Getting Started Module Objectives
Upon successful completion of the Getting Started Learning Module students will:
1. Locate the title for the required text for the course and make sure you have that text the first
day of class.
2. Demonstrate how to acce
Logic Chapter 5
Name
_
Use Boolean Properties to simplify the following:
1. (A A) U = _
2. (C C) = _
3. (A A) A = _
4. (B ) B = _
5. (A C) (B C) = _
6. (A C) C = _
7. (B A) (BA) = _
8. (A B) (A B) = _
9. (A B) (C B) = _
10. (A B) (B C) = _
Blog and Avatar Learning Activity
Before beginning this learning activity, upload a personal avatar to the My
Places area of your course. An avatar is a personal image that can be used
to represent a user throughout Blackboard Learn. Follow the instructio
Chapter 5 The Logic of Sets, II Learning Objectives
1. The Learner/Student will Name and Define Boolean (Set-Theory) properties
2. The Learner/Student will be able to simplify expressions using Boolean properties.
3. The Learner/Student will be able to si
LOGIC HOMEWORK CHAPTER 5
Simplify the Set Notations using Boolean Properties to their lowest terms
Use a separate sheet of paper to work out!
1.
(AB) (BA) = _
2.
(AB) B = _
3.
[(AB) (AB)] A = _
4.
[(AB) (AC) (AB)] = _
5.
A (BA) = _
6.
(A(BC) (BA)C) = _
7.